Normal air diffusion through walls of a pneumatic rubber tire reduces tire pressure within the internal cavity of the tire over time. For this invention, an annular circular groove is provided in the sidewall of the tire in which contains a flexible (e.g. rubber) tube which is secured within the groove with a rubber coating and for which the tube acts to pump atmospheric air into the internal cavity of the pneumatic tire to aid in providing (e.g. maintaining) air pressure in the internal cavity of the pneumatic tire by alternating (e.g. sequential segmental) pressure impressed upon the tube by flexing of the tire, particularly the tire sidewall, during operation of the tire in service such as during vehicular operation of the tire.